The presence of speckle in ultrasound images makes it hard to segment them using active contours. Speckle causes the energy function of the active contours to have many local minima, and the gradient descent procedure used for evolving the contour gets trapped in these minima. A new algorithm, called tunnelling descent, is proposed in this paper for evolving active contours. Tunnelling descent can jump out of many of the local minima that gradient descent gets trapped in. Experimental results with 70 short axis cardiac ultrasound images show that tunnelling descent has no trouble finding the blood-tissue boundary (the endocardium). This holds irrespective of whether tunnelling descent is initialized in blood or tissue.